- 6635 South Hall
There exist few families of examples of Riemannian manifolds with positive sectional curvature. In dimensions above 24, the only known examples are metrics on spheres and projective spaces. In searching for new examples, it is natural to study metrics which are invariant under a large group of symmetries. This has led to many topological obstructions to the existence of highly symmetric metrics of positive curvature. We will review some of the conjectures in the subject and results that provide evidence for these conjectures in the presence of symmetry.